(a) Field of the Invention
The present invention relates generally to belief functions and, more specifically, to a method for automatically learning belief functions.
(b) Description of Related Art
A system may have multiple information sources which are used to make a decision. In a target recognition situation, the information source may take the form of a radar sensor/detector. For example, three different sensors may be used when attempting to distinguish targets from decoys. A complication arises when two of the sensors report that an object under surveillance is a target, and the third sensor reports that the object is a decoy. This complication must be resolved to accurately recognize the object.
The Dempster-Shafer theory of evidential reasoning, which is known to those skilled in the art, provides means of combining information from different, and possibly contradictory information sources. The Dempster-Shafer theory uses explicit representations of ignorance and conflict to avoid the shortcomings of classical Bayesian probability calculus. Dempster-Shafer theory uses belief functions (also called basic probability assignments or bpa's), which are generalizations of discrete probability functions used in Bayesian probability calculus. In Dempster-Shafer theory, bpa's represent the distribution of probability mass in a system (i.e, how strongly something is believed, based on the information that has been provided). Referring back to the target recognition problem, an example bpa for the sensor information available may be .mu..sub.1 ({target})=0.55,({target, decoy})=0.45. This bpa represents the fact that 55% of the evidence from a set of sensors considered supports the conclusion that the observed object is a target, the remaining 45% remains uncommitted between the target and the decoy. Multiple sets of sensors may be used to measure various characteristics of an object. For example, the bpa .mu..sub.1 may be based on sensors that determine the shape of the object being monitored. A second set of sensors used to produce .mu..sub.2 may be based on object size, while a third bpa .mu..sub.3 may be based on sensors that monitor the heat associated with the object. Each set of sensors is used to determine the identity of the object being observed by using different characteristics of the object. Each bpa represents a probability distribution as to the certainty of the identity of an object. Sets containing more than a single element (in this example, target and decoy) are used to represent ambiguity or confusion. Empty sets are used to represent conflict or disagreement of evidence. Belief functions may be combined to provide information for further conclusions. For example, bpa's generated based on size, shape, and heat may be combined to reach a decision on the identity of the object under surveillance.
Previous applications of Dempster-Shafer theory include expert systems, accounting systems, and sensor fusion. Despite previous applications and the utility of Dempster-Shafer theory, there is no automatic method for adjusting belief functions in a system. The ability to adjust the belief functions used in a system would allow the system to "learn" from the information provided by information sources. The ability of a system to automatically update belief functions would, in addition to improving the performance of the system, allows a system to determine erroneous information sources, inappropriate information combinations, and optimal information granularities. Therefore, there exists the need for a method of automatically updating belief functions.